// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
#define EIGEN_SPECIALFUNCTIONS_FUNCTORS_H

namespace Eigen {

namespace internal {

/** \internal
 * \brief Template functor to compute the incomplete gamma function igamma(a, x)
 *
 * \sa class CwiseBinaryOp, Cwise::igamma
 */
template<typename Scalar>
struct scalar_igamma_op : binary_op_base<Scalar, Scalar>
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const
	{
		using numext::igamma;
		return igamma(a, x);
	}
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
	{
		return internal::pigamma(a, x);
	}
};
template<typename Scalar>
struct functor_traits<scalar_igamma_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasIGamma
	};
};

/** \internal
 * \brief Template functor to compute the derivative of the incomplete gamma
 * function igamma_der_a(a, x)
 *
 * \sa class CwiseBinaryOp, Cwise::igamma_der_a
 */
template<typename Scalar>
struct scalar_igamma_der_a_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_der_a_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const
	{
		using numext::igamma_der_a;
		return igamma_der_a(a, x);
	}
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
	{
		return internal::pigamma_der_a(a, x);
	}
};
template<typename Scalar>
struct functor_traits<scalar_igamma_der_a_op<Scalar>>
{
	enum
	{
		// 2x the cost of igamma
		Cost = 40 * NumTraits<Scalar>::MulCost + 20 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasIGammaDerA
	};
};

/** \internal
 * \brief Template functor to compute the derivative of the sample
 * of a Gamma(alpha, 1) random variable with respect to the parameter alpha
 * gamma_sample_der_alpha(alpha, sample)
 *
 * \sa class CwiseBinaryOp, Cwise::gamma_sample_der_alpha
 */
template<typename Scalar>
struct scalar_gamma_sample_der_alpha_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_gamma_sample_der_alpha_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& alpha, const Scalar& sample) const
	{
		using numext::gamma_sample_der_alpha;
		return gamma_sample_der_alpha(alpha, sample);
	}
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& alpha, const Packet& sample) const
	{
		return internal::pgamma_sample_der_alpha(alpha, sample);
	}
};
template<typename Scalar>
struct functor_traits<scalar_gamma_sample_der_alpha_op<Scalar>>
{
	enum
	{
		// 2x the cost of igamma, minus the lgamma cost (the lgamma cancels out)
		Cost = 30 * NumTraits<Scalar>::MulCost + 15 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasGammaSampleDerAlpha
	};
};

/** \internal
 * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
 *
 * \sa class CwiseBinaryOp, Cwise::igammac
 */
template<typename Scalar>
struct scalar_igammac_op : binary_op_base<Scalar, Scalar>
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const
	{
		using numext::igammac;
		return igammac(a, x);
	}
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
	{
		return internal::pigammac(a, x);
	}
};
template<typename Scalar>
struct functor_traits<scalar_igammac_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasIGammac
	};
};

/** \internal
 * \brief Template functor to compute the incomplete beta integral betainc(a, b, x)
 *
 */
template<typename Scalar>
struct scalar_betainc_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_betainc_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x,
																  const Scalar& a,
																  const Scalar& b) const
	{
		using numext::betainc;
		return betainc(x, a, b);
	}
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const
	{
		return internal::pbetainc(x, a, b);
	}
};
template<typename Scalar>
struct functor_traits<scalar_betainc_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasBetaInc
	};
};

/** \internal
 * \brief Template functor to compute the natural log of the absolute
 * value of Gamma of a scalar
 * \sa class CwiseUnaryOp, Cwise::lgamma()
 */
template<typename Scalar>
struct scalar_lgamma_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const
	{
		using numext::lgamma;
		return lgamma(a);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::plgamma(a); }
};
template<typename Scalar>
struct functor_traits<scalar_lgamma_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasLGamma
	};
};

/** \internal
 * \brief Template functor to compute psi, the derivative of lgamma of a scalar.
 * \sa class CwiseUnaryOp, Cwise::digamma()
 */
template<typename Scalar>
struct scalar_digamma_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const
	{
		using numext::digamma;
		return digamma(a);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pdigamma(a); }
};
template<typename Scalar>
struct functor_traits<scalar_digamma_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasDiGamma
	};
};

/** \internal
 * \brief Template functor to compute the Riemann Zeta function of two arguments.
 * \sa class CwiseUnaryOp, Cwise::zeta()
 */
template<typename Scalar>
struct scalar_zeta_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x, const Scalar& q) const
	{
		using numext::zeta;
		return zeta(x, q);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x, const Packet& q) const
	{
		return internal::pzeta(x, q);
	}
};
template<typename Scalar>
struct functor_traits<scalar_zeta_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasZeta
	};
};

/** \internal
 * \brief Template functor to compute the polygamma function.
 * \sa class CwiseUnaryOp, Cwise::polygamma()
 */
template<typename Scalar>
struct scalar_polygamma_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& n, const Scalar& x) const
	{
		using numext::polygamma;
		return polygamma(n, x);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& n, const Packet& x) const
	{
		return internal::ppolygamma(n, x);
	}
};
template<typename Scalar>
struct functor_traits<scalar_polygamma_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasPolygamma
	};
};

/** \internal
 * \brief Template functor to compute the error function of a scalar
 * \sa class CwiseUnaryOp, ArrayBase::erf()
 */
template<typename Scalar>
struct scalar_erf_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const { return numext::erf(a); }
	template<typename Packet>
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const
	{
		return perf(x);
	}
};
template<typename Scalar>
struct functor_traits<scalar_erf_op<Scalar>>
{
	enum
	{
		PacketAccess = packet_traits<Scalar>::HasErf,
		Cost = (PacketAccess
#ifdef EIGEN_VECTORIZE_FMA
					// TODO(rmlarsen): Move the FMA cost model to a central location.
					// Haswell can issue 2 add/mul/madd per cycle.
					// 10 pmadd, 2 pmul, 1 div, 2 other
					? (2 * NumTraits<Scalar>::AddCost + 7 * NumTraits<Scalar>::MulCost +
					   scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
#else
					? (12 * NumTraits<Scalar>::AddCost + 12 * NumTraits<Scalar>::MulCost +
					   scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
#endif
					// Assume for simplicity that this is as expensive as an exp().
					: (functor_traits<scalar_exp_op<Scalar>>::Cost))
	};
};

/** \internal
 * \brief Template functor to compute the Complementary Error Function
 * of a scalar
 * \sa class CwiseUnaryOp, Cwise::erfc()
 */
template<typename Scalar>
struct scalar_erfc_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const
	{
		using numext::erfc;
		return erfc(a);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::perfc(a); }
};
template<typename Scalar>
struct functor_traits<scalar_erfc_op<Scalar>>
{
	enum
	{
		// Guesstimate
		Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasErfc
	};
};

/** \internal
 * \brief Template functor to compute the Inverse of the normal distribution
 * function of a scalar
 * \sa class CwiseUnaryOp, Cwise::ndtri()
 */
template<typename Scalar>
struct scalar_ndtri_op
{
	EIGEN_EMPTY_STRUCT_CTOR(scalar_ndtri_op)
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a) const
	{
		using numext::ndtri;
		return ndtri(a);
	}
	typedef typename packet_traits<Scalar>::type Packet;
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pndtri(a); }
};
template<typename Scalar>
struct functor_traits<scalar_ndtri_op<Scalar>>
{
	enum
	{
		// On average, We are evaluating rational functions with degree N=9 in the
		// numerator and denominator. This results in 2*N additions and 2*N
		// multiplications.
		Cost = 18 * NumTraits<Scalar>::MulCost + 18 * NumTraits<Scalar>::AddCost,
		PacketAccess = packet_traits<Scalar>::HasNdtri
	};
};

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
